Multiply the following complex numbers: $({-3i}) \cdot ({-4-5i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3i}) \cdot ({-4-5i}) = $ $ ({0} \cdot {-4}) + ({0} \cdot {-5}i) + ({-3}i \cdot {-4}) + ({-3}i \cdot {-5}i) $ Then simplify the terms: $ (0) + (0i) + (12i) + (15 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (0 + 12)i + 15i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (0 + 12)i - 15 $ The result is simplified: $ (0 - 15) + (12i) = -15+12i $